Page - 64 - in Adaptive and Intelligent Temperature Control of Microwave Heating Systems with Multiple Sources

3. ModelingMicrowaveHeating Estimationpartwithk≥2 : [Kn(k−1)] = [Pnp(k−1)] [Jn(k−1)]T([Jn(k−1)][Pnp(k−1)] · [Jn(k−1)]T+σ2 [IM] )−1 , [Φne(k−1)] = [ Φnp(k−1) ] +[Kn(k−1)] ( Ψnr(k−1) −VT(k−1)[Pnp(k−1)]V(k−1)), [Pne(k−1)] = ( [IM]− [Kn(k−1)][Jn(k−1)] )[ Pnp(k−1) ] , (3.68) with [Jn(k−1)] := V(k−1)VT(k−1). According to equation 3.67, at each timek the estimated effective matrix Φne(k−1) is expected to be equivalent to Φn(k), and then usedfor thepredictionof future temperatures. 3.3. Black-boxModeling Although grey-box modeling is simple to implement and control, it hasseveralconstraints, suchasthefixedtypeofsetup(figure 3.1)and restrictions such as the assumptions 1 and 2. Compared with the grey-box modeling, black-box modeling is much more flexible, with- outanyrestrictions inthesetuptype. Inorder toenhancetheadaptiv- ityofthetemperaturecontrolsystemandimprovethemodelaccuracy, theblack-boxmodelingapproach isalsoapplied. The scope of black-box structures is diverse, covering methods from neural networks, radial basis networks, wavelet networks, to fuzzy logic models. These different methods are used not only for model- ing, but also for pattern classification, controller design, self-learning systems, and artificial intelligence systems. The principle used in most black-box methods is a two-layer mapping. The first mapping 64